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On the b-invariant of a normal graded ring

  • Aryaman Maithani
  • Anurag K. Singh
  • Kei-ichi Watanabe
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Abstract

The b-invariant of a normal graded ring was defined recently by Okuma, Watanabe, and Yoshida. We study this for invariant rings of finite groups, proving that it is nonpositive in the case of abelian groups, but not necessarily otherwise; more generally, we give a description of the anticanonical module for invariant rings of finite groups. Turning to infinite groups, we record the anticanonical module and the b-invariant for families of determinantal rings. We also construct standard-graded Cohen-Macaulay rings of characteristic zero, with isolated singularities and negative b-invariant, that are not of strongly F-regular type, thereby disproving a conjecture of Okuma-Watanabe-Yoshida.

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Cite

BibTeXRIS
BibTeX
@misc{maithani2026binvariant,
  title = {{On the $b$-invariant of a normal graded ring}},
  author = {Aryaman Maithani and Anurag K. Singh and Kei-ichi Watanabe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.32003},
  eprint = {2609.32003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32003},
}
RIS
TY  - UNPB
TI  - On the b-invariant of a normal graded ring
AU  - Aryaman Maithani
AU  - Anurag K. Singh
AU  - Kei-ichi Watanabe
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.32003
UR  - https://arxiv.org/abs/2609.32003
AB  - The b-invariant of a normal graded ring was defined recently by Okuma, Watanabe, and Yoshida. We study this for invariant rings of finite groups, proving that it is nonpositive in the case of abelian groups, but not necessarily otherwise; more generally, we give a description of the anticanonical module for invariant rings of finite groups. Turning to infinite groups, we record the anticanonical module and the b-invariant for families of determinantal rings. We also construct standard-graded Cohen-Macaulay rings of characteristic zero, with isolated singularities and negative b-invariant, that are not of strongly F-regular type, thereby disproving a conjecture of Okuma-Watanabe-Yoshida.
ER  -